Kinetic Molecular Theory and the Ideal Gas Law

We have just seen how each of the gas laws conceptually follows from kinetic molecular theory. We can also derive the ideal gas law from the postulates of kinetic molecular theory. In other words, the kinetic molecular theory is a quantitative model that implies PV = nRT. Let s now explore this derivation. 

From Newton s second law, the force (F) associated with an individual collision is given by F = ma, where m is the mass of the particle and a is its acceleration as it changes its direction of travel due to the collision. The acceleration for each collision is the change in velocity (Av) divided by the time interval (At), so the force imparted for each collision 

If a particle collides elastically with the wall, it bounces off the wall with no loss of energy. For a straight-line collision, the change in velocity is 2v (the particle s velocity was V before the collision and —v after the collision therefore, the change is 2v). The force per collision is given by  

The total number of collisions in the time interval A t on a wall of snrface area A is proportional to the number of particles that can reach the wall in this time interval—in other words, all particles within a distance of v A t of the wall. These particles occnpy a volume given by v A t X A, and their total number is equal to this volume multiplied by the density of particles in the container (n/V)  

FIGURE S.17 The Pressure ott the Wall of a Contairrer The pressure on the wall of a container can be calculated by determining the total force due to collisions of the particles with the wall. 

---